The objective of this proposal is the development and evaluation of statistical methods for use in research related to studies of Human Immunodeficiency Virus (HIV) disease and the AIDS epidemic. A collaborative team from the University of California, Berkeley, and the University of California, San Francisco, will be involved in the project. Three topic areas are of specific interest. The first relates to detailed development of the backcalculation method for projection of AIDS incidence counts and estimation of HIV prevalence, including comparison with other techniques. The second is concerned with the evaluation of the potential effects of vaccines for control of HIV epidemics, including assessment of the necessary vaccination coverage and the relationships between length of immunity, behavioral changes and revaccination policies. Finally, further methodological work is proposed related to attempts to describe the natural history of HIV disease. Of particular interest are statistical techniques that (i) consider data on specific AIDS diagnoses such as Kaposi's sarcoma and related temporal phenomena, (ii) quantify the evolution of immunological marker variables during disease progression, (iii) use marker variables to improve the use of data in therapeutic trials and relate such variables to certain outcomes, such as the onset of AIDS and (iv) the description of properties of HIV infectivity with emphasis on variation in infectiousness over disease stages. All methods will be applied to various data sets where appropriate.